Fourier methods have extensive applications in the study of fine properties of the collision operator. These methods have being used to show propagation of Sobolev norms for the homogeneous Boltzmann equation in [1]} under the restriction \(b\in L^{2}(\mathbb {S}^{d-1})\) , based in a result of [2]}. In the work [3]} Fourier methods has being used in full potential to prove propagation of Sobolev regularity for general \(b\in L^{1}(\mathbb {S}^{d-1})\) .
